Short's character was allegedly based on Brandt, and the two do seem to share a likeness. The sensationalist story is that the portrayal on the Netflix series drove the doctor to suicide, but his publicist Jacquie Trachtenberg told press that simply wasn't the case:

The show definitely deeply hurt him, he was being made fun of because of the way he looks... It is mean, and it was bullying. But the show was not the reason for his depression, and it was not the reason he would take his own life.

I can imagine the portrayal on The Unbreakable Kimmy Schmidt was hurtful, and it's unfortunate that the parody came at a time where Brandt was so clearly struggling. However, as Trachtenberg made clear, the joke made at Brandt's expense is allegedly not the reason for his death.

As we know, depression isn't simple, and while it's heartbreaking that Brandt was hurt by these jokes, we shouldn't blame the series outright for his actions. What we should take from Brandt's tragedy is a reminder to help the people in our lives struggling with mental illness and to get them as much help as we possibly can. Suicide is all too common, and hopefully Brandt's death can spring people to action in the right ways.